document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310853>Question 310853</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve the trig equation  sin2x = sqrt(3)sinx </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #225711 by </B><A HREF=/tutors/aboutme.mpl?userid=J2R2R><B>J2R2R(94)</B></A><img src=\"/images/stars/stars-08.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=J2R2R><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=J2R2R><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=225711\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Solve the trig equation sin(2x) = sqrt(3)sin(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "sin(2x) = 2 sin(x) cos(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we have\r<BR>\n" );
document.write( "\n" );
document.write( "2 sin(x) cos(x) = sqrt(3) sin(x)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "We can cancel sin(x) from both sides which makes sin(x) = 0 a solution i.e. 0, 180, 360, etc.\r<BR>\n" );
document.write( "\n" );
document.write( "2 cos(x) = sqrt(3) or cos(x) = sqrt(3)/2 giving x=30 and 330.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So solutions in degrees in the range 0<=x<360 are\r<BR>\n" );
document.write( "\n" );
document.write( "0, 30, 180 and 330\r<BR>\n" );
document.write( "\n" );
document.write( "which shows there are four solutions for each 360 degrees range.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "N.B. bear in mind that a 360 degree range does not take both end points in its range since one end point is the other end point with 360 added to it. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );